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Making decisions with unknown sensory reliability.

Deneve S - Front Neurosci (2012)

Bottom Line: Most of the time, we cannot know this reliability without first observing the decision outcome.We consider here a Bayesian decision model that simultaneously infers the probability of two different choices and at the same time estimates the reliability of the sensory information on which this choice is based.We show that this model can account for recent findings in a motion discrimination task, and can be implemented in a neural architecture using fast Hebbian learning.

View Article: PubMed Central - PubMed

Affiliation: Département d'Etudes Cognitives, Group for Neural Theory, Ecole Normale Supérieure Paris, France.

ABSTRACT
To make fast and accurate behavioral choices, we need to integrate noisy sensory input, take prior knowledge into account, and adjust our decision criteria. It was shown previously that in two-alternative-forced-choice tasks, optimal decision making can be formalized in the framework of a sequential probability ratio test and is then equivalent to a diffusion model. However, this analogy hides a "chicken and egg" problem: to know how quickly we should integrate the sensory input and set the optimal decision threshold, the reliability of the sensory observations must be known in advance. Most of the time, we cannot know this reliability without first observing the decision outcome. We consider here a Bayesian decision model that simultaneously infers the probability of two different choices and at the same time estimates the reliability of the sensory information on which this choice is based. We show that this can be achieved within a single trial, based on the noisy responses of sensory spiking neurons. The resulting model is a non-linear diffusion to bound where the weight of the sensory inputs and the decision threshold are both dynamically changing over time. In difficult decision trials, early sensory inputs have a stronger impact on the decision, and the threshold collapses such that choices are made faster but with low accuracy. The reverse is true in easy trials: the sensory weight and the threshold increase over time, leading to slower decisions but at much higher accuracy. In contrast to standard diffusion models, adaptive sensory weights construct an accurate representation for the probability of each choice. This information can then be combined appropriately with other unreliable cues, such as priors. We show that this model can account for recent findings in a motion discrimination task, and can be implemented in a neural architecture using fast Hebbian learning.

No MeSH data available.


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Simplified Bayesian model and “diffusion” model with changing priors. (A) Average integrated input divided by the threshold  as a function of time in the diffusion model at low coherence (c = 0.2). Plain Lines: the two choices are a priori equiprobable (Lo = 0). Dashed line: B is a priori more probable than A (Lo = −0.6). Dotted line: A is a priori more probable than B (Lo = 0.6). In the diffusion model, the prior is implemented by a constant offset of the decision variable, i.e., a different starting point for integration. (B) The same as in (A) for medium motion coherence (c = 1). (C) Log odds divided by the decision threshold [i.e., L/Dopt (ĉ)] for the simplified Bayesian decision model at low coherence (c = 0.2). Dashed, dotted and plain lines correspond to different priors [same as in (A)] (D). Same as (C) but for a high value of motion coherence (c = 2).
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Figure 5: Simplified Bayesian model and “diffusion” model with changing priors. (A) Average integrated input divided by the threshold as a function of time in the diffusion model at low coherence (c = 0.2). Plain Lines: the two choices are a priori equiprobable (Lo = 0). Dashed line: B is a priori more probable than A (Lo = −0.6). Dotted line: A is a priori more probable than B (Lo = 0.6). In the diffusion model, the prior is implemented by a constant offset of the decision variable, i.e., a different starting point for integration. (B) The same as in (A) for medium motion coherence (c = 1). (C) Log odds divided by the decision threshold [i.e., L/Dopt (ĉ)] for the simplified Bayesian decision model at low coherence (c = 0.2). Dashed, dotted and plain lines correspond to different priors [same as in (A)] (D). Same as (C) but for a high value of motion coherence (c = 2).

Mentions: By adjusting the sensory weights and decision thresholds on-line as a function of the coherence estimate, the Bayesian decision model constantly re-evaluates the influence of the prior during the entire duration of the trial. The effect of the prior is thus much more than setting the starting point for sensory integration. In particular, this can paradoxically make the prior appears as an additional “sensory evidence,” as illustrated in Figure 5. While the diffusion model (Figures 5A,B) starts integration at a level set by the prior, but later behaves as a simple integrator, the influence of the prior in the Bayesian model (Figures 5C,D) is amplified during the trial. This strongly resembles a change in the drift rate, as if the priors were in fact an additional “pseudo” motion signal.


Making decisions with unknown sensory reliability.

Deneve S - Front Neurosci (2012)

Simplified Bayesian model and “diffusion” model with changing priors. (A) Average integrated input divided by the threshold  as a function of time in the diffusion model at low coherence (c = 0.2). Plain Lines: the two choices are a priori equiprobable (Lo = 0). Dashed line: B is a priori more probable than A (Lo = −0.6). Dotted line: A is a priori more probable than B (Lo = 0.6). In the diffusion model, the prior is implemented by a constant offset of the decision variable, i.e., a different starting point for integration. (B) The same as in (A) for medium motion coherence (c = 1). (C) Log odds divided by the decision threshold [i.e., L/Dopt (ĉ)] for the simplified Bayesian decision model at low coherence (c = 0.2). Dashed, dotted and plain lines correspond to different priors [same as in (A)] (D). Same as (C) but for a high value of motion coherence (c = 2).
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Figure 5: Simplified Bayesian model and “diffusion” model with changing priors. (A) Average integrated input divided by the threshold as a function of time in the diffusion model at low coherence (c = 0.2). Plain Lines: the two choices are a priori equiprobable (Lo = 0). Dashed line: B is a priori more probable than A (Lo = −0.6). Dotted line: A is a priori more probable than B (Lo = 0.6). In the diffusion model, the prior is implemented by a constant offset of the decision variable, i.e., a different starting point for integration. (B) The same as in (A) for medium motion coherence (c = 1). (C) Log odds divided by the decision threshold [i.e., L/Dopt (ĉ)] for the simplified Bayesian decision model at low coherence (c = 0.2). Dashed, dotted and plain lines correspond to different priors [same as in (A)] (D). Same as (C) but for a high value of motion coherence (c = 2).
Mentions: By adjusting the sensory weights and decision thresholds on-line as a function of the coherence estimate, the Bayesian decision model constantly re-evaluates the influence of the prior during the entire duration of the trial. The effect of the prior is thus much more than setting the starting point for sensory integration. In particular, this can paradoxically make the prior appears as an additional “sensory evidence,” as illustrated in Figure 5. While the diffusion model (Figures 5A,B) starts integration at a level set by the prior, but later behaves as a simple integrator, the influence of the prior in the Bayesian model (Figures 5C,D) is amplified during the trial. This strongly resembles a change in the drift rate, as if the priors were in fact an additional “pseudo” motion signal.

Bottom Line: Most of the time, we cannot know this reliability without first observing the decision outcome.We consider here a Bayesian decision model that simultaneously infers the probability of two different choices and at the same time estimates the reliability of the sensory information on which this choice is based.We show that this model can account for recent findings in a motion discrimination task, and can be implemented in a neural architecture using fast Hebbian learning.

View Article: PubMed Central - PubMed

Affiliation: Département d'Etudes Cognitives, Group for Neural Theory, Ecole Normale Supérieure Paris, France.

ABSTRACT
To make fast and accurate behavioral choices, we need to integrate noisy sensory input, take prior knowledge into account, and adjust our decision criteria. It was shown previously that in two-alternative-forced-choice tasks, optimal decision making can be formalized in the framework of a sequential probability ratio test and is then equivalent to a diffusion model. However, this analogy hides a "chicken and egg" problem: to know how quickly we should integrate the sensory input and set the optimal decision threshold, the reliability of the sensory observations must be known in advance. Most of the time, we cannot know this reliability without first observing the decision outcome. We consider here a Bayesian decision model that simultaneously infers the probability of two different choices and at the same time estimates the reliability of the sensory information on which this choice is based. We show that this can be achieved within a single trial, based on the noisy responses of sensory spiking neurons. The resulting model is a non-linear diffusion to bound where the weight of the sensory inputs and the decision threshold are both dynamically changing over time. In difficult decision trials, early sensory inputs have a stronger impact on the decision, and the threshold collapses such that choices are made faster but with low accuracy. The reverse is true in easy trials: the sensory weight and the threshold increase over time, leading to slower decisions but at much higher accuracy. In contrast to standard diffusion models, adaptive sensory weights construct an accurate representation for the probability of each choice. This information can then be combined appropriately with other unreliable cues, such as priors. We show that this model can account for recent findings in a motion discrimination task, and can be implemented in a neural architecture using fast Hebbian learning.

No MeSH data available.


Related in: MedlinePlus